13-Write a grammar for the language consisting of strings that have n copies of the letter a followed by the same number of copies of the letter b and the the same number of copies of the letter c, where n >0. For example, the strings abc, aaaabbbbcccc, and aaaaaaaabbbbbbbbcccccccc are in the language but a, abbc, bac, and aaabbbcc are not

(15) Let M be the language over {a, b, c, d, e, f} accepting all strings so that: 1. There are precisely two e's in the string. 2. Every a is immediately followed by an even number of b's. 3. Every c is immediately followed by an odd number of f's. b's and f's don't occur except as provided in rules 2 and 3. 5. All c's occur after the first e. 4. 6. All a's occur before the second e. 7. In between the two e's there are exactly twice as many c's as a's. Construct a context-free grammar generating M. You do not need an inductive proof, but you should explain how your construction accounts for each rule. 5) We could eliminate one rule from M and make it regular. Which one? Why? (5) Show that the class of context free languages is not closed under intersection by finding two CFLS whose intersection is not a CFL.

Let E = {a, b, c}. Write a grammar that generates the language: L = {c"ww* a":n > 0, m > 0, w e E+} HTML EditorÉ B I UA A 工E 三三 x x, : You Tube T T 12pt Paragraph G= ( {S,A}, {a,b,c}, S, P) P: S-> cSalcAa A->aAa|cAc 18 words

Rewrite the grammar below to eliminate left recursion.S-> S + A | AA -> A * B | BB -> (S) | id